Linked Questions

9
votes
3answers
6k views

Difference between spinor and vector field [duplicate]

How do we distinguish spinors and vector fields? I want to know it in terms of physics with mathematical argument.
2
votes
1answer
6k views

What is the difference between a tensor, vector, and a matrix? [duplicate]

I'm currently going through notes on a physics course and I'm having trouble understanding the difference between a tensor, a vector, and a matrix. I know that a vector is a kind of tensor and that a ...
1
vote
1answer
549 views

Difference between scalars, vectors, matrices and tensors [duplicate]

What is the difference between a scalar, vector, matrix and tensor in simple terms? Are vector fields and tensors related?
20
votes
5answers
8k views

Why would Klein-Gordon describe spin-0 scalar field while Dirac describe spin-1/2?

The derivation of both Klein-Gordon equation and Dirac equation is due the need of quantum mechanics (or to say more correctly, quantum field theory) to adhere to special relativity. However, excpet ...
27
votes
2answers
4k views

Introduction to spinors in physics, and their relation to representations

First, I shall say that I am familiar with the intuitive idea that a spinor is like a vector (or tensor) that only transforms "up to a sign" when acted on by the rotation group. I have even rotated a ...
17
votes
1answer
11k views

What is a spinor? [closed]

In a youtube video, sir Michael Atiyah mentioned that even after working during the most of his life on spinors, he doesn't know what a spinor is. Now surely that was part of his humorous introduction ...
6
votes
1answer
1k views

Equivalent definitions of vectors

Equivalent definitions of vectors. In maths a vector is an object that obeys some axioms of a vector space. But in physics a vector can be thought as an object which is invariant under rotations of ...
2
votes
1answer
2k views

General definition of vector, spinor, and spin

I am looking for basic and exact definitions of fundamental physical concepts in graduate level. I reach this following definitions. Could you please help to improve these definitions. Spin: ...
0
votes
1answer
1k views

What's the difference between spinor and spin?

Some related information might be found here: What is the difference between a spinor and a vector or a tensor? and Wikipedia seemed to have an explanation but was not very clear. From what I read, ...
1
vote
2answers
335 views

Is a vector field not a vector quantity?

I'm trying to make sense of Poisson bracket relation $$\{L_i,A_k\}_{PB}~=~\epsilon_{ikl}A_l,\tag1$$ where $L_i$ is $i$th component of angular momentum, $A_k$ is $k$th component of an arbitrary ...
4
votes
1answer
603 views

How quantum field transforms in case of some particular spin

Except when a particle is spin-0, field of all particles transforms when frame of reference is changed, and this defines what spin is. The question is, specifically how does the quantum field ...
3
votes
1answer
453 views

Motivation for spinors

After it was found that the gamma matrices couldn't be Pauli matrices and only had to be larger and even, why was their need to define a new algebraic object (i.e a Dirac spinor)? Why couldn't a ...
2
votes
1answer
147 views

(Lorentz etc) invariant vector fields

(Background: I know some but not much differential geometry, hopefully enough to formulate this post.) I want to ask about what physicists mean when they say scalar, vector, etc. The answer in ...